# All Polynomial-equation-solver Formulas List

#### Formula:

x = (- b ± √ b2 - 4 x a x c) / 2 x a

Where,

a = Coefficient of x2
b = Coefficient of x
c = Constant

## Cubic Equation Formula

#### Cubic Equation Formula:

x1=(- term1 + r13*cos(q3/3) )
x2=(- term1 + r13*cos(q3+(2*Π)/3) )
x3=(- term1 + r13*cos(q3+(4*Π)/3) )

Where,

discriminant(Δ) = q3 + r2
term1 = √(3.0)*((-t + s)/2)
r13= 2 * √(q)
q = (3c- b2)/9
r = -27d + b(9c-2b2)
s = r + √(discriminant)
t = r - √(discriminant)

## Quartic Equation

#### Quartic Equation Formula:

Quartic Equation : ax4 + bx3 + cx2 + dx + e = 0
NOTE : Let p and q be the square root of any 2 non-zero roots.
p = sqrt(y1)
q = sqrt(y3)
r = -g / (8pq)
s = b / (4a)
x1 = p + q + r - s
x2 = p - q - r - s
x3 = -p + q - r - s
x4 = -p - q + r - s

#### Formula:

Δ = b2 − 4 × a × c

Where,
Δ = Discriminant Value
a = Coefficient of x2
b = Coefficient of x
c = Constant

## Completing the Square

#### Formula:

Step 1 : Move the constant number over to the other side
Step 2 : Divide all the terms by a coefficient of x^2.
Step 3 : Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation.
Step 4 : Convert the left-hand side to squared form, and simplify the right-hand side.
Step 5 : Solve for x value (Add for x1 and Subtract for x2)

#### Formula:

x1,2 = -2c / (b + √ (b2 - 4ac)
y1,2 = -2c / (b - √ (b2 - 4ac)

Where,

y1,2 = Solution in Subtraction
a,b,c = Real Constant

## Discriminant and Cubic Root

#### Formula:

p = (1/3) [(3c/a) - (b2) / a2) ]
q = (1/27) [ (2b3 / a3) - (9bc / a2) + (27e / a) ]
D = (p/3)3 + (q/2)2

If D value is greater than 0:

u = [ (-q/2) + D1/2 ] 1/3
v = [ (-q/2) - D1/2 ] 1/3
x = u+v
s = [- (u+v)/2 ]
t = [(u-v / 2) * 31/2]
y = s+t
z = s-t

If D value is less than 0:

Φ = acos [ (-q/2) (|p| / 3) -3/2 ]
x = 2 [ (|p| / 3)1/2 cos (Φ/3) ]
y = -2 [ (|p| / 3)1/2 cos (Φ + π)/3 ]
z =-2 [ (|p| / 3)1/2 cos (Φ - π)/3 ]

Where,

D = Discriminant
p,q = Real Constant
a,b,c,e = Real Constant
x,y,z = Cubic root
u,v = Real Constant
s,t = Temp Variable
cos = Cosine
Φ = Angle

#### Formula:

x = (- b ± √ b2 - 4 * a * c) / (2 * a)

Where,

a,b,c = Attributes

## 4th Degree Equation Solver

#### Quartic Equation Formula:

Quartic Equation : ax4 + bx3 + cx2 + dx + e = 0
NOTE : Let p and q be the square root of any 2 non-zero roots.
p = sqrt(y1)
q = sqrt(y3)
r = - g / (8pq)
s = b / (4a)
x1 = p + q + r - s
x2 = p - q - r - s
x3 = -p + q - r - s
x4 = -p - q + r - s

## Gregory Newton

#### Formula:

f(x + a) = n=0 Σ ( (a)n Δn f(x) ) / n!

## Prediction Equation

#### Formula :

Prediction Equation(y) = a + mx
Slope(m) = (N x ∑XY - (∑Xm)(∑Ym)) / (N x ∑X2 - (∑X)2)
Intercept(a) = (∑Ym - b(∑Xm))

Where,

x and y are the variables.
m = The slope of the regression line
a = The intercept point of the regression line and the y axis.
N = Number of values or elements
X = First Data Set
Y = Second Data Set
∑XY = Sum of the Product of First and Second Data Set
∑Xm = Mean of First (X) Data Set
∑Ym = Sum of Second (Y) Data Set
∑X2 = Sum of Square of First (X) Data Set Values
x = Number of duration/Valdity